Geodesic
New a~priori estimates for $q$-nonlinear elliptic systems with strong nonlinearities in the gradient, $1$
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 35, Tome 310 (2004), pp. 19-48

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We consider $q$-nonlinear nondiagonal elliptic systems, $1$, with strong nonlinear terms in the gradient. Under a smallness condition on the gradient of a solution in the Morry space $L^{q,n-q}$, we estimate $L^p$-norm of the gradient, $p>q$, and the Hölder norm of the solution for the case $n=2$. An abstract theorem on “quasireverse Hölder inequalities” proved by the author earlier is essencially used. 
@article{ZNSL_2004_310_a1,
     author = {A. A. Arkhipova},
     title = {New a~priori estimates for $q$-nonlinear elliptic systems with strong nonlinearities in the gradient, $1<q<2$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {19--48},
     publisher = {mathdoc},
     volume = {310},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_310_a1/}
}
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A. A. Arkhipova. New a~priori estimates for $q$-nonlinear elliptic systems with strong nonlinearities in the gradient, $1